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Simplifying 0 = 2x4 + 4x3 + -48x2 Reorder the terms: 0 = -48x2 + 4x3 + 2x4 Solving 0 = -48x2 + 4x3 + 2x4 Solving for variable 'x'. Remove the zero: 48x2 + -4x3 + -2x4 = -48x2 + 4x3 + 2x4 + 48x2 + -4x3 + -2x4 Reorder the terms: 48x2 + -4x3 + -2x4 = -48x2 + 48x2 + 4x3 + -4x3 + 2x4 + -2x4 Combine like terms: -48x2 + 48x2 = 0 48x2 + -4x3 + -2x4 = 0 + 4x3 + -4x3 + 2x4 + -2x4 48x2 + -4x3 + -2x4 = 4x3 + -4x3 + 2x4 + -2x4 Combine like terms: 4x3 + -4x3 = 0 48x2 + -4x3 + -2x4 = 0 + 2x4 + -2x4 48x2 + -4x3 + -2x4 = 2x4 + -2x4 Combine like terms: 2x4 + -2x4 = 0 48x2 + -4x3 + -2x4 = 0 Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(24 + -2x + -1x2) = 0 Factor a trinomial. 2x2((4 + -1x)(6 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {0, 4, -6}
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